Recent progress in fluctuation theorems and free energy recovery

Abstract

Abstract. In this note we review recent progress about fluctuation relations and their applicability to free energy recovery in single molecule experiments. We underline the importance of the operational definition for the mechanical work and the non-invariance of fluctuation relations under Galilean transformations, both aspects currently amenable to experimental test. Finally we describe a generalization of the Crooks fluctuation relation useful to recover free energies of partially equilibrated states and thermodynamic branches. NONEQUILIBRIUM SMALL SYSTEMSIn 1944 Erwin Schrödinger published the classic monography What is life? where he pointed out the importance of physical and chemistry laws to understand living systems [1]. The notion that genetic information should be encoded in an "aperiodic crystal" seeded the subsequent discovery of the double helix structure of DNA. Chapter 7 of Schrödinger's monography contains an interesting discussion about the similarities and differences between a clockwork motion and the functioning of an organism. According to Schrödinger the regular motion of a clock must be secured by a weak spring. Yet, whatever the weakness of the spring is, it will produce frictional effects that do compensate for the external driving of the clock (e.g. the battery) in order to secure its regular motion. Being friction a statistical phenomenon he concludes that the regular motion of the clock cannot be understood without statistical mechanics. Then he further states: For it must not believed that the driving mechanism really does away with the statistical nature of the process. The true physical picture includes the possibility that even a regularly going clock should all at once invert its motion and, working backward, rewind its own spring -at the expense of the heat of the environment. The event is just 'still a little less likely' than a 'Brownian fit' of a clock without driving mechanism.Recent advances in microfabrication techniques, detection systems and instrumentation have made possible the measurement of such "inverted motions" referred by Schrödinger. The controlled manipulation and detection of very small objects makes possible to exert and measure tiny forces applied on them and follow their trajectories in space-time with resolution of piconewtons, nanometers and microseconds respectively.

Meaning of temperature in different thermostatistical ensembles

“…It takes little effort to verify that equations (2.5)-(2.7) hold exactly for standard classical ergodic Hamiltonian systems with an arbitrary number of degrees of freedom N. Similarly, the canonical ensemble discussed below can be applied to (sub)systems of any size. These mathematical facts are widely appreciated by many colleagues [9,[12][13][14][15]18,19,21]-in particular those interested in understanding DNA folding [24], microscopic information storage and erasure [25] and fluctuation phenomena [26]-and yet remain ignored by a few others [23,27]. When judged objectively, there is no doubt that the application of thermodynamic concepts to finite systems has considerably advanced our understanding of biophysical, colloidal and quantum processes.…”

Anomalous Fluctuation Relations

“…1 -2012/6/7 -19:43 -page 2 2 ten years has shown that FRs hold for a great variety of systems thus featuring one of the rare statistical physical principles that is valid even very far from equilibrium: see summaries in [13,14,15,16,17,18] for stochastic processes, [19,20,21,22,23,24] for deterministic dynamics and [25,26] for quantum systems. Many of these relations have meanwhile been verified in experiments on small systems, i.e., systems on molecular scales featuring only a limited number of relevant degrees of freedom [27,28,29,30,31,32], cf. the Chapters by Ciliberto et al, Alemany et al, and Sagawa and Ueda.…”

How nanomechanical systems can minimize dissipation

“…Our aim is to derive the optimal control strategy over the class of smooth potential forces for the problem adapted to the Second Law of Thermodynamics. From the experimental slant, smooth potentials model macroscopic degrees of freedom of the system whose state is determined by external sources [16]. We show that our problem is well-posed when regarded as the limit of a more general control problem which takes into account the energy cost of the control.…”